Analytical predictions of concrete pumping: Extending the Khatib–Khayat model to Herschel–Bulkley and modified Bingham fluids

It has been widely reported that self-compacting concrete and other cement-based materials are shear-thickening materials. However, there is a lack of an analytical model on the prediction of flow rate–pressure drop relation in the pumping of concrete that takes into account both the presence of the lubrication layer and the shear-thickening behavior of fresh concrete. This work fills this gap by extending analytical predictions of concrete pumping in the presence of a lubrication layer to nonlinear rheological models including the Herschel–Bulkley model and the modified Bingham model. In doing so, a new method is developed to obtain the flow rate–pressure drop relation for the steady Hagen–Poiseuille coaxial flow of two immiscible, incompressible fluids. Analytical expressions are presented for the flow rate–pressure drop relation, shear rate distribution, and velocity distribution based on the two-fluid Herschel–Bulkley model and separately based on the two-fluid modified Bingham model. With those analytical expressions, volumetric flow rate vs. pressure loss curves can be readily constructed, given values for the other eight quantities: three for the rheological properties of the bulk concrete, three for the rheological properties of the fluid in the lubrication layer, pipe radius, and thickness of the lubrication layer.